frequency distribution

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frequency distribution

[¦frē·kwən·sē ‚dis·trə′byü·shən]
(mathematics)
A function which measures the relative frequency or probability that a variable can take on a set of values.
Frequency distributionclick for a larger image
Fig. 10 Frequency distribution.

frequency distribution

the number of times each value of a variable occurs in a set of observations.

A frequency-distribution table is a simple way of representing sociological observations. It consists of at least two columns: the left-hand one contains the values which a variable may take, and the right-hand one contains the number of times each value occurs. An additional right-hand column can also be included to show the percentage distribution. In Fig. 10 the number of male and female respondents to a questionnaire are shown. see also BAR CHART. HISTOGRAM. PIE CHART, which can also be used to represent distributions.

Frequency Distribution

 

a set of the various numerical values of some quantitative characteristic of the members of a population where an indication is given of the frequency of each value—that is, the size of the corresponding group of these members is indicated. A frequency distribution expresses the result of the grouping of the members of the population with respect to a single quantitative characteristic. If the values are ordered, that is, arranged according to increasing or decreasing magnitude, then the frequency distribution is said to be ranked.

A distinction is made between discrete and interval frequency distributions. A discrete frequency distribution is based on a discontinuously varying grouping characteristic; an example is the distribution of workers with respect to the number of machine tools operated. An interval, or grouped (that is, reduced to groups), frequency distribution is based on a continuously varying characteristic; an example of this type is the distribution of a group of people with respect to age. Frequency distributions can also be grouped in the case of a discrete characteristic if the range of this characteristic is sufficiently great—for example, the distribution of urban communities with respect to the number of residents.

The intervals of the grouping characteristic may be equal or unequal. If unequal, they usually increase progressively; this case arises when qualitatively different types of phenomena are being singled out. The sizes of the groups formed are indicated in the frequency distribution by absolute numbers, or frequencies; by relative numbers, or relative frequencies, which are usually percentages of the total; or by both, in two parallel columns. The ratios of the frequencies or relative frequencies to the sizes of the corresponding intervals are called the distribution density.

The importance of frequency distributions in statistics is great. A well-constructed frequency distribution makes possible a detailed analysis of the structure of the population with respect to a given characteristic. Thus, the groups into which the population breaks down can be determined. In addition, the nature of the distribution of the members of the population with respect to the given characteristic can be ascertained—for example, whether the distribution is symmetric or asymmetric or what the degree of concentration of the members is. Finally, various statistics can be calculated, such as the range of the characteristic (the absolute difference between the maximum and the minimum value), the average value of the characteristic, the deviations from the average value, the degree of skewness of the frequency distribution, and the measure of kurtosis (the degree of closeness of a cluster of values of the characteristic around the average value). For easy comprehension, a frequency distribution can be represented graphically in a rectangular coordinate system in the form of a frequency polygon, histogram, cumulative frequency polygon, or ogive. Various combinations of frequency distributions for a population can be presented in the form of statistical tables.

I. G. VENETSKII

References in periodicals archive ?
On table 5, we have the phoneme frequency distributions for the NWS and BCW texts, together with the one that comes from the EFE corpus.
In environmental sciences, use of one kind of data from different sites to form homogeneous regions from these sites with respect to some common hydrological and geographical features and further to estimate the suitable frequency distribution of these homogenous regions gives shape to RFA (Hosking and Wallis, 1997).
8) was tested with different frequency distributions.
Then the frequency distribution of the array of values of the function [(z/v).
Frequency distribution of arch forms according to Noroozi's mathematical formula is shown in table 1,
frequency distribution by minimum radius (mm) Wood species 260-280 281-310 311 -340 Nothofagus cunninghamii 42 11 5 Pinus radiata 68 11 5 Acacia melanoxylon 53 12 18 Atherosperma moschatum 81 0 0 Eucalyptus saligna 0 21 32 E.
6) It is perhaps worth noting that the frequency distributions presented by Baumgardner, et al.
The incubation period for SARS is likely to be varied, with the frequency distribution being nonnormal (Figure 1).
All things considered, the primary aim of this article has been to demonstrate that the use of the traditional expression of the Gini index is not recommended when dealing with nonunitary frequency distributions, since this has been originally developed for situations in which the frequencies are unitary.
This is good news because many secondary data sources, for example, most census reports, publish tables containing frequency distributions but generally do not present the raw data.
As it is believed that word uses have a less skewed, and therefore more even, frequency distribution when compared to word senses, it is concluded that the improvement in retrieval effectiveness reported by Schutze and Pedersen is due to this difference in the frequency distributions.
The discussion by Qin addresses the problem of preprocessing and cleansing textual data for discovering semantic patterns in keyword frequency distributions.

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